Data sharpening can reduce bias in non-parametric regression and density estimation. Firth’s (1993) approach to bias reduction through adjustment of the score function provides an underlying framework for data sharpening and extensions, such as sharpened derivative estimation in kernel regression.

A closed-form expression for the remaining life expectancy based on the gamma-Gompertz model has been derived recently in the literature. However, the closed-form expression available to users is not correct. We provide, therefore, a valid and correct expression for the life expectancy at age x by using elementary calculus. We also consider a comparative numerical study by using real data to confirm

With a bound on cost and bounds on stratum sample sizes, a cost weighted objective function is decomposed to reveal a general simple exact optimal sample allocation algorithm for minimizing sampling variances. Some known allocation methods are special cases.

We prove the consistency of the ℓ1 penalized negative binomial regression (NBR). A real data application about German health care demand shows that the ℓ1 penalized NBR produces a more concise but more accurate model, comparing to the classical NBR.

Kotlarski (1967) establishes a fundamental result on identification of marginal distributions of independent random variables X, Y, and Z from the joint distribution of random variables (U,V), where (U,V)=(X+Z,Y+Z). We extend this result to the case (U,V)=(X+aZ1+bZ2,Y+cZ1+dZ2), where Z1 and Z2 are identically distributed, and a, b, c, and d are different weights. As an outgrowth of the proof, we also

In this article, we propose model-free marginal and conditional feature screening approaches for ultra-high dimensional competing risks data. The suggested procedures possess ranking consistency and sure screening properties. Their finite-sample performances are verified through numerical studies.

Independently scattered random measures are usually defined and constructed under the additional condition of being infinitely divisible, a rather strong condition. A more natural condition is the assumption that the random measure has no atoms, that is being atomless. We show that atomless random measures on δ-rings are necessarily infinitely divisible, so infinite divisibility is in fact a quite

A new measure of dispersion is presented here that generalizes entropy for positive data. It is intrinsically linked to a measure of central tendency and is determined by the data through a power transformation that best symmetrizes the observations.

When functional data are observed on parts of the domain, it is of interest to recover the missing parts of curves. Kraus (2015) proposed a linear reconstruction method based on ridge regularization. Kneip and Liebl (2019) argue that an assumption under which Kraus (2015) established the consistency of the ridge method is too restrictive and propose a principal component reconstruction method that

We study the properties of an M-estimator arising from the minimization of an integrated version of the quantile loss function. The estimator depends on a tuning parameter which controls the degree of robustness. We show that the sample median and the sample mean are obtained as limit cases. Consistency and asymptotic normality are established and a link with the Hodges–Lehmann estimator and the Wilcoxon

Considering G as a countable infinite group and μ a symmetric probability on it whose support generates G, and calling μ a generating measure of G. Here, we prove that for some probability μ, group G admits a long-range percolation phase transition in which the corresponding percolation threshold λc(μ) is finite. Consequently, the group invariant λc(G)=infμλc(μ) is well-defined, where the infimum is

This paper develops sufficient conditions for the preservation of WSAI, RWSAI and LWSAI under increasing transformations on the coordinates, respectively. Applications of the preservation in the asset allocation problem are presented as well.

In this note we introduce a sequence of bilinear operators that unify ergodic averages and backward martingales in a nontrivial way. We establish its convergence in a range of Lp-norms and leave its a.s.convergence as an open problem. This problem shares some similarities with a well-known unresolved conjecture on a.s.convergence of double ergodic averages with respect to two commuting transformations

We develop Edgeworth expansion theory for spot volatility estimator under general assumptions on the log-price process that allow for drift and leverage effect. The result is based on further estimation of skewness and kurtosis, when compared with existing second order asymptotic normality result. Thus our theory can provide with a refinement result for the finite sample distribution of spot volatility

We study a multi-armed bandit problem with covariates in a setting where there is a possible delay in observing the rewards. Under some reasonable assumptions on the probability distributions for the delays and using an appropriate randomization to select the arms, the proposed strategy is shown to be strongly consistent.

The asymptotic log-Harnack inequality is established for SPDE with degenerate multiplicative noise by the coupling method. As applications, the gradient estimate, asymptotic strong Feller property, irreducibility, heat kernel estimate and ergodicity are derived.

This article describes a class of invariant Markov processes on certain totally disconnected groups. An invariant pseudodifferential operator on these groups, similar to the Vladimirov operator on the p-adic line, allows us to state an L2-abstract Cauchy problem for a homogeneous heat-type pseudodifferential equation. The fundamental solutions of these parabolic-type pseudodifferential equations give

We use the ideas of maximum mean discrepancy and ranks of nearest neighbors to propose some tests of independence among multiple random vectors of arbitrary dimensions. Numerical studies demonstrate that proposed tests can outperform the existing tests in various examples.

Fractional factorial designs are popularly used in different fields of experimentations, which allow experimenters to study large number of potentially relevant factors with relatively small number of experimental units but suffer from the fact that some of the effects are aliased with some others. In order to overcome these drawbacks, the foldover technique is widely used to de-alias factor effects

Stable subordinators, and more general subordinators possessing power law probability tails, have been widely used in the context of subdiffusions, where particles get trapped or immobile in a number of time periods, called constant periods. The lengths of the constant periods follow a one-sided distribution which involves a parameter between 0 and 1 and whose first moment does not exist. This paper

Rotated sphere packing design is constructed by scaling, rotating and translating the lattice that has asymptotically lowest fill distance, its space-filling properties are very well. Currently, it can only be used for experimental design in hypercube. In this paper, we generalize the sphere packing design to simplex, which is the domain of experimental design with mixtures. In order to use the lattice

We consider the last passage percolation on the complete graph. Let Gn=([n],En) be the complete graph on vertex set [n]={1,2,…,n}, and i.i.d. sequence {Xe:e∈En} be the passage times of edges. Denote by Wn the largest passage time among all self-avoiding paths from 1 to n. First, it is proved that Wn∕n converges to constant μ, where μ is called the time constant and coincides with the essential supremum

A Bayesian model may be relied on to the extent of its adequacy by minimizing the posterior expected loss raised to the power of a discounting exponent. The resulting action is minimax under broad conditions when the sample size is held fixed and the discounting exponent is infinite. On the other hand, for any finite discounting exponent, the action is Bayes when the sample size is sufficiently large

The BDS test is a test for detecting whether a random sequence is i.i.d. (independent and identically distributed). It has been used in economics and finance to examine whether a fitted time series model is adequate by examining whether the residual sequence is nearly i.i.d. Though the BDS test is widely used in the literature, it has a weakness of over-rejecting the null hypothesis even though the

Passing–Bablok regression relies on the slopes of the connecting lines between pairwise measurements. We introduce the Block–Passing–Bablok regression for grouped data, where repeated measurements with errors in both variables are available.

The so-called mixed-type atomic decomposition theorems are established for martingale weak Hardy–Morrey spaces wHMp,ϕs, wHMp,ϕ∗ and wHMp,ϕS, respectively. As applications, a sufficient condition for sublinear operators on martingale weak Hardy–Morrey spaces to be bounded is given. In particular, some classical martingale inequalities, including Burkholder’s inequality, are extended to the case of the

Stochastic approximation of a given time series {∑j=1kXjYj} by a linear combination of simpler sequences {∑j=1kXj} and {∑j=1kYj} is treated uniformly over k∈{1,…,n}. A maximal inequality is proven in order to find a sharp bound on Value-at-Risk of max1≤k≤n|∑j=1kXjYj|.

We give an equivalence-singularity criterion for infinite products of Cauchy measures under simultaneous shifts of the location and scale parameters. Our result is an extension of Lie and Sullivan’s result giving an equivalence-singularity criterion under dilations of scale parameters. Our proof utilizes McCullagh’s parametrization of the Cauchy distributions and maximal invariant, and a closed-form

In this note we prove a novel characterization result stating that any distribution is determined uniquely up to an additive constant by its conditional variance function where the conditioning is based on double quantile trimming. We also outline potential statistical applications of the proposed characterization.

In this paper, using the coupling by change of measure and Krylov’s estimate, we establish the dimension-free Harnack inequalities for stochastic heat equation with Neumann boundary condition. Compared with the existing results, we only need to assume that the nonlinearity b satisfies a suitable integrability condition. As an application, we also give the distribution properties of the solution of

For Y=‖aZ+θ‖2, a>0, Z∼Np(θ,Ip), θ≠{0}, we show that the distribution of Y is not stochastically ordered in a>0. We provide extensions to spherically symmetric, elliptically symmetric, and skew-normal distributions, as well as to other quadratic forms.

We give explicitly the probability density of the local time of the Brox diffusion at first passage times. Such formula is used to find the moments and to relate the minima and maxima of the environment to the most and least visited points of the diffusion.

In this article we study the asymptotic behavior of the realized quadratic variation of a process ∫0tusdGsH, where u is a Hölder continuous process with order β>1−H and GH is a self-similar Gaussian process with parameter H∈(0,3∕4). We prove almost sure convergence uniformly in time and a stable weak convergence for the realized quadratic variation. As an application, we construct strongly consistent

Consider the following class of conformable time-fractional stochastic equation, for any x∈R fixed, Tα,tau(x,t)=λσ(u(x,t))Ẇt,t∈[a,∞),0<α<1, with a non-random initial condition u(x,0)=u0(x),x∈R assumed to be non-negative and bounded, Tα,ta is a conformable time-fractional derivative, σ:R→R is globally Lipschitz continuous, Ẇt a generalized derivative of Wiener process and λ>0 is the noise level. Given

Optimal Transport (OT) distances result in a powerful technique to compare the probability distributions. Defining a similarity measure between clusters has been an open problem in Statistics. This paper introduces a hierarchical clustering algorithm using the OT based distance measures and analyzes the performance of the proposed algorithm on standard datasets with respect to the existing and popular

Recently, there is an increasing interest to study number theory by using large and moderate deviations from probability theory. In this paper, we prove the large and moderate deviation principles for the Erdös–Kac theorem in the polynomial rings of finite fields, which extends the results of Mehrdad and Zhu (2016).

Optimal designs for the within-group estimator of the coefficients in panel data linear regressions are investigated on the design space of unity cube. Identical uniform designs on partial vertexes of this cube selected by 2-level orthogonal arrays are proved to be D-, A- and E-optimal.

Some distribution functions have been characterized based on two non-adjacent generalized and dual generalized order statistics. Moreover, we show that these characterization properties provide a beneficial strategy to predict future events, which are based on past or current events and on an arbitrary distribution function.

In this paper, we consider the stochastic periodic averaging principle for impulsive neutral stochastic functional differential equations with non-Lipschitz coefficients. By using the theory of stochastic analysis and elementary inequalities, we show that the solutions of impulsive neutral stochastic functional differential equations converge to the solutions of the corresponding averaged neutral stochastic

We prove a new Bernstein-type inequality for the log-likelihood function of Bernoulli variables. In contrast to classical Bernstein’s inequality and Hoeffding’s inequality when applied to this log-likelihood, the new bound is independent of the parameters of the Bernoulli variables and therefore does not blow up as the parameters approach 0 or 1. The new inequality strengthens certain theoretical results

We propose a U-statistics test for regression coefficients in high dimensional partially linear models. In addition, the proposed method is extended to test part of the coefficients. Asymptotic distributions of the test statistics are established. Simulation studies demonstrate satisfactory finite-sample performance.

Suppose Vν is the pseudo-variance function of the Cauchy-Stieltjes Kernel (CSK) family K+(ν) generated by a non degenerate probability measure ν with support bounded from above. We determine the formula for pseudo-variance function (or variance function Vν in case of existence) under boolean additive convolution power. This formula is used to identify the relation between variance functions under Boolean

This paper deals with one-dimensional anticipated backward stochastic differential equations where the coefficient is left-Lipschitz in y and the anticipated term of y⋅. The existence of solutions to the equation as well as a comparison theorem is obtained.

Let b